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Two Dimensional Monte Carlo Device Simulation

Two Dimensional Monte Carlo Device Simulation. Jason Harris http://www.goodnet.com/~smegtra Arizona State University Faculty Advisor: Dragica Vasileska. Presentation Overview. Project Schedule Overview of Completed Work Discussion of Coding Benefits Description of New Approaches

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Two Dimensional Monte Carlo Device Simulation

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  1. Two Dimensional Monte Carlo Device Simulation Jason Harris http://www.goodnet.com/~smegtra Arizona State University Faculty Advisor: Dragica Vasileska

  2. Presentation Overview • Project Schedule • Overview of Completed Work • Discussion of Coding Benefits • Description of New Approaches • Overview of Remaining Work

  3. Project Schedule • Spring, 1999: Learn theory, write a bulk Monte Carlo simulator for GaAs, write a 1-D Poisson solver • Summer 1999: Write a 2-D Poisson solver, convert Monte Carlo simulator to use non-parabolic bands • Fall 1999: Couple the Monte Carlo simulator and the Poisson solver and perform device simulations

  4. GaAs Dispersion Relationship

  5. Bulk Monte Carlo Simulator • Object-Oriented coding is very flexible • Non-Parabolic band model • One scattering table for each equivalent dispersion valley

  6. Scattering Mechanisms • Acoustic Deformation Potential • Polar Optical Phonon Absorption/Emission • Intervalley Absorption/Emission • Intravalley Absorption/Emission • Fictitious Self-Scattering

  7. Bulk Monte Carlo Simulator Flowchart

  8. One Dimensional Poisson Solver • Object-Oriented coding is very flexible • Uses LU-Decomposition • Dirichlet and Neumann boundary conditions • Uses uniform mesh spacing

  9. Two-Dimensional Poisson Solver • Object-Oriented design promotes code flexibility • Uses SOR to solve Poisson’s Equation • Uniform mesh spacing • Code is present for 3-D mesh with non-uniform mesh spacing

  10. The Infamous “Pseudo-Dot”

  11. “Pseudo-Dot” Results

  12. “Pseudo-Dot” Top View

  13. Mesh Object FacilitatesCreating Devices • Construct object with a description of the bulk material • Create rectangular solids within the device with arbitrary material properties • Creating the “pseudo-dot” requires only six function calls

  14. Mesh Object is Flexible • Mesh points can have multiple boundary conditions associated with them • ‘Smart’ mesh edges makes creating devices easier • Code is designed for non-uniform, three dimensional meshes

  15. Node Points are Comprehensive • Intrinsic concentration (code is ready for heterostructures) • Dielectric constant • Doping profile • Temperature

  16. Pointers are my Friends • Mesh point material descriptions • Scattering tables • Measurement methods • C++ dynamic memory allocation used for carrier injection

  17. ‘Smart’ Pointers Used Extensively • Keep track of objects accessing a particular memory location in order to avoid memory leaks • Free memory location only after last accessor has released it • Ten assembly language instructions for creating • Four assembly language instructions for copy • Six assembly language instructions for deleting

  18. Carrier Object • Position vector (three-dimensional) • Momentum vector (three-dimensional) • Associated scattering table • Can be mixed with the Mesh object to easily pinpoint device region transitions

  19. Encapsulated Scattering Tables • Encapsulate a complete scattering table inside of another scattering table in order to speed up processing and reduce computation • For example, devices with non-uniform doping

  20. Encapsulation in a GaAs Device • Valley-Dependent mechanisms - there are three choices • Ionized Impurity - as many choices as there are doping regions • Fictitious Self-Scattering

  21. Why aren’t you watching the animation?

  22. Using EncapsulatedScattering Tables • Concrete mechanism • Meta-Mechanism • Root Mechanism

  23. Fractional Meta-Carriers • Carriers in a two-dimensional Monte Carlo are actually meta-carriers composed of many statistically identical carriers • Scattering tables give the statistical behavior of a single carrier, but they are also valid for a meta-carrier composed of statistically similar individual carriers

  24. Fractional Meta-Carriers • Free-Flight routine should use the meta-carrier’s mass and charge instead of an individual carrier’s mass & charge • Since we need to track the number of individual carriers in each meta-carrier anyway, why not simplify the charge assignment scheme?

  25. Fractional Meta-Carriers • When solving Poisson’s Equation, meta-carriers are split and placed on the nodes • Split the meta-carriers into smaller meta-carriers and place these on the nodes • Combine with any other new meta-carriers placed on that node which is in the same valley

  26. Why aren’t you watching the animation?

  27. Remaining Work • Charge assignment scheme • Carrier injection • Transfer Poisson solver from continuity model to device model • Debugging - simulate a text-book MOSFET

  28. Two Dimensional Monte Carlo Device Simulation Jason Harris http://www.goodnet.com/~smegtra Arizona State University Faculty Advisor: Dragica Vasileska

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